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2 years ago

5

Three friends decide to share the cost to rent an apartment equally. The apartments that they are considering cost at least 1 20

0 per month. Write and solve an inequality to represent each person's share of the rental cost

1 answer:

deff fn [24]2 years ago

5 0

Each persons share of rental will cost at least 400$ per month!!

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A farmer wants to build a rectangular pen and then divide it with two interior fences. The total area inside of the pen will be

irina [24]

Answer:

Dimensions of the pen:

x = 11 ft

y = 6 ft

Step-by-step explanation:

Let call "x" and "y" dimensions of the rectangular pen and x > y, so the interior fences will be equal to y.

The exterior length is 2*x + 2*y and its cost is (2*x + 2*y ) *20.40

The interior fences are 2*y and its cost is 2*y* 17

Total cost C = (2*x + 2*y ) *20.40 + 2*y* 17 (1)

Now area inside the pen is 66 ft² and it is equal to:

A = x*y ⇒ 66 = x*y ⇒ y = 66/x

Plugging that value in equation (1) will give C as a function of x

C(x) = [ 2*x + 2* (66/x) ]* 20.40 + 2* (66/x) * 17

C(x) = ( 2*x + 132/x ) 20.40 + 2244/x

C(x) = 40,80*x + 2692.8/x + 2244/x

C(x) = 40.80*x + 4936,8/x

Taking derivatives on both sides of the equation we get

C´(x) = 40.80 - 4936,8/x²

C´(x) = 0 ⇒ 40.80 - 4936,8/x² = 0 ⇒ 40.80 *x² = 4936,8

x² = 4936,8 / 40.80 ⇒ x² = 121 ⇒ x √121

x = 11 ft

And y = 66/x ⇒ y = 66/11 ⇒ y = 6 ft

3 0

4 years ago

Solve the equation for x.

aliina [53]

Answer:

X is equal to 7

Step-by-step explanation:

Open parenthesis.

3/4x +63/4=21/2

take common denominator

3/4x=42/4-63/4

Solve

3/4x=-21/4

3x=21

x=7

7 0

3 years ago

Find the area of the shape shown below.

hichkok12 [17]

Answer:

26.75 units ^2

Step-by-step explanation:

Since the shape is complex, divide it into 3 right angled triangles and one square. Find the area of these individual shapes first, then fin the sum of these area to calculate the ultimate area of e complex shape:

Triangle 1 = 1/2 x 2 x 5 = 5 units ^2

Triangle 2 = 1/2 x 2 x 2 = 2 units ^2

Triangle 3 = 1/2 x 3.5 x 9 = 15.75 units ^2

Square = 2 x 2 = 4 units squared.

Now add all these up 15.75 + 2 + 5 + 4 = 26.75 units squared.

Hope this helps

6 0

3 years ago

Solve the following system of eq ions. Express your answer as an ordered

daser333 [38]

Answer:

(3,2)

Step-by-step explanation:

3x + 4y=17

- 4x – 3y= - 18

Multiply the first equation by 4

4(3x + 4y=17 )

12x +16y = 68

Multiply the second equation by 3

3( - 4x – 3y= - 18)

-12x -9y = -54

Add the new equations together to eliminate x

12x +16y = 68

-12x -9y = -54

-----------------------

7y = 14

Divide by 7

7y/7 = 14/7

y=2

Now find x

3x+4(2) = 17

3x+8 = 17

Subtract 8 from each side

3x+8-8 = 17-8

3x = 9

Divide by 3

x = 3

7 0

3 years ago

Bad gums may mean a bad heart. Researchers discovered that 79% of people who have suffered a heart attack had periodontal diseas

zysi [14]

Answer:

(A) 0.297

(B) 0.595

Step-by-step explanation:

Let,

H = a person who suffered from a heart attack

G = a person has the periodontal disease.

Given:

P (G|H) = 0.79, P(G|H') = 0.33 and P (H) = 0.15

Compute the probability that a person has the periodontal disease as follows:

$P(G)=P(G|H)P(H)+P(G|H')P(H')\\=P(G|H)P(H)+P(G|H')(1-P(H))\\=(0.79\times0.15)+(0.33\times(1-0.15))\\=0.399$

(A)

The probability that a person had periodontal disease, what is the probability that he or she will have a heart attack is:

$P(H|G)=\frac{P(G|H)P(H)}{P(G)}\\=\frac{0.79\times0.15}{0.399} \\=0.29699\\\approx0.297$

Thus, the probability that a person had periodontal disease, what is the probability that he or she will have a heart attack is 0.297.

(B)

Now if the probability of a person having a heart attack is, P (H) = 0.38.

Compute the probability that a person has the periodontal disease as follows:

$P(G)=P(G|H)P(H)+P(G|H')P(H')\\=P(G|H)P(H)+P(G|H')(1-P(H))\\=(0.79\times0.38)+(0.33\times(1-0.38))\\=0.5048$

Compute the probability of a person having a heart attack given that he or she has the disease:

$P(H|G)=\frac{P(G|H)P(H)}{P(G)}\\=\frac{0.79\times0.38}{0.5048}\\ =0.59469\\\approx0.595$

The probability of a person having a heart attack given that he or she has the disease is 0.595.

4 0

3 years ago